Question

Orange juice is bottled on two different production lines. A sample of 5 bottles from the first line yields a mean of 1.2 quarts with a standard deviation of 0.02 quarts, and a sample of 6 bottles from the second line yields a mean of 1.15 quarts with a standard deviation of 0.01 quarts. The test statistic is equal to which of the following?

Answer 1

Since we are dealing with 2 samples that both have small sample sizes, then we are looking for the t-statistic.

Assuming the conditions are valid for this problem, we first find the difference between the two averages, so 1.2-1.15=0.05

Next, we find the pooled standard deviation:
sp^2=[((n1−1)s1^2)+((n2−1)s2^2)]/[n1+(n2−2)]
sp^2=[((5-1)*0.02^2)+((6-1)*0.01^2)]/[5+(6-2)]
sp^2=[4(0.0004)+5(0.0001)]/[5+4]
sp^2=[0.0016+0.0005]/[9]
sp^2=0.0021/9
sp^2=0.00023333
sp=0.01528

Lastly, we find our t-statistic:
t = [difference of group averages / standard error of difference]
t = 0.05/[0.01528sqrt(1/5 + 1/6)]
t = 5.4039

So, our test statistic is t = 5.4039 approximately